The PipeQual model is based on ecological theory and describes stand and tree growth as a result of carbon acquisition and allocation (Mäkelä 1997, 2002).

The model consists of four modules, STAND, CROBAS, WHORL and BRANCH, through which tree metabolism, tree structure and stand dynamics are interconnected in the framework of carbon balance at an annual time resolution (Fig. 1 ). The stand is described as a distribution of tree size classes. Each class is represented by its mean tree and stocking density.

Annual photosynthetic production is first computed for the whole stand and then allocated to trees using a modified Lambert-Beer equation (Duursma and Mäkelä 2007). This is input to the CROBAS module where the growth of trees is derived from the carbon balance of the mean tree of the size class. The mean tree acquires carbon, respires, and loses biomass through turnover. Growth is allocated to foliage, branches, stem, coarse roots and fine roots to maintain a regular structure derived from the pipe model (Shinozaki et al. 1964a,b), profile theory (Chiba et al. 1988) and fractal crown allometry (Mäkelä and Sievänen 1992; Duursma et al. 2010). These regularities allow for tracking the development of dimensional variables in addition to the biomass variables.

Climate and site impacts enter the model through (1) tissue-specific rates of carbon fluxes and (2) carbon allocation coefficients. Through modularity of model structure, different submodels may be chosen to describe these processes. Mäkelä et al. (2016) incorporated these effects in PipeQual under current climate by means of effective temperature sum (ETS) and site type (as defined by Cajander 1949). Potential gross primary production depends on ETS because temperature, radiation (photosynthetically active radiation, PAR) and vapour pressure deficit (VPD) correlate with each other while soil water availability only plays a minor role Norway spruce in Finland under current climate (Härkönen et al. 2010; Minunno et al. 2016).

Growth respiration in the model is proportional to net production while maintenance respiration depends on the biomass of different compartments, air temperature and nitrogen concentration of tissue (through site type). Tissue life span is also related to climate and nitrogen content. Mäkelä et al. (2016) demonstrated that the consequent climate and soil driven geographic trends of forest carbon balance components yielded accurate estimates of the productivity of Norway spruce stands in Fenno–Scandian conditions.

PipeQual has been parameterised for Scots pine (Mäkelä and Mäkinen 2003) and for Norway spruce (Kantola et al. 2007). It has been tested against data from permanent sample plots (Kalliokoski et al. 2016) and from ecological measurement sites (Mäkelä et al. 2016). Some key applications of PipeQual have been to maximising the economic revenue from harvests, taking into account wood quality (Hyytiäinen et al. 2004, Niinimäki et al. 2012, 2013), and to carbon sequestration under changing climate (Mäkipää et al. 2015)


Kantola A., Mäkinen H. and Mäkelä A. 2007. Stem form and branchiness of Norway spruce as sawn timber – predicted by a process-based model. For Ecol. Manage 241:209-222.

Hyytiäinen K., Hari, P. Kokkila T., Mäkelä A., Tahvonen O. and Taipale J. 2004. Connecting a process-based forest growth model to stand-level economic optimization. Canadian Journal of Forest Research 34:2060-2073

Mäkelä A and Mäkinen H. (2003) Generating 3D sawlogs with a process-based growth model. Forest Ecology and Management 184:337-354

Mäkipää, R., Linkosalo, T., Komarov, A., Mäkelä, A. 2015. Mitigation of climate change with biomass harvesting in Norway spruce stands –– are harvesting practices carbon neutral? Canadian Journal of Forest Research 45: 217–225. dx.doi.org/10.1139/cjfr-2014-0120.

Niinimäki S., Tahvonen O., Mäkelä A. 2012. Applying a process-based model in Norway spruce management. Forest Ecology and Management 265:102-115.

Niinimäki S., Tahvonen O, Mäkelä A. and Linkosalo T. 2013. On the economics of Norway spruce stands and carbon storage. Canadian Journal of Forest Research 7: 637-648.

Härkönen S., Pulkkinen M., Duursma R.A., Mäkelä A. 2010. Estimating annual GPP, NPP and stem growth in Finland using summary models. For. Ecol. Manage. 259: 524-533.

Kalliokoski T., Mäkinen H., Linkosalo T., Mäkelä A. 2016. Evaluation of stand-level hybrid PipeQual model with permanent sample plot data of Norway spruce. Canadian Journal of Forest Research 47:234-245.

Mäkelä A., Pulkkinen M., Mäkinen H. 2016. Bridging empirical and carbon-balance based forest site productivity - significance of below-ground allocation. Forest Ecology and Management 372:64-77.

Minunno F, Peltoniemi M, Launiainen S, Aurela M, Mammarella I, Lindroth A, Lohela A, Minkkinen K, Mäkelä A 2016. Calibration and validation of a semi-empirical flux ecosystem model for coniferous forests in the Boreal region. Ecological Modelling 341:37-52.